diff --git a/cyclotomic.cabal b/cyclotomic.cabal
--- a/cyclotomic.cabal
+++ b/cyclotomic.cabal
@@ -1,5 +1,5 @@
 Name:                cyclotomic
-Version:             0.4.1
+Version:             0.4.2
 Synopsis:            A subfield of the complex numbers for exact calculation.
 Description:         The cyclotomic numbers are a subset of the
                      complex numbers that are represented exactly, enabling exact
diff --git a/src/Data/Complex/Cyclotomic.hs b/src/Data/Complex/Cyclotomic.hs
--- a/src/Data/Complex/Cyclotomic.hs
+++ b/src/Data/Complex/Cyclotomic.hs
@@ -1,12 +1,15 @@
 {-# OPTIONS_GHC -Wall #-}
+{-# LANGUAGE Trustworthy #-}
 
--- Module      :  Data.Complex.Cyclotomic
--- Copyright   :  (c) Scott N. Walck 2012
--- License     :  GPL-3 (see LICENSE)
--- Maintainer  :  Scott N. Walck <walck@lvc.edu>
+{- | 
+Module      :  Data.Complex.Cyclotomic
+Copyright   :  (c) Scott N. Walck 2012-2013
+License     :  GPL-3 (see LICENSE)
+Maintainer  :  Scott N. Walck <walck@lvc.edu>
+Stability   :  experimental
 
-{- | The cyclotomic numbers are a subset of the complex numbers with
-     the following properties:
+The cyclotomic numbers are a subset of the complex numbers with
+the following properties:
     
      1.  The cyclotomic numbers are represented exactly, enabling exact
      computations and equality comparisons.
@@ -64,8 +67,12 @@
     ,sqrtRat
     ,sinDeg
     ,cosDeg
+    ,sinRev
+    ,cosRev
     ,gaussianRat
     ,polarRat
+    ,polarRatDeg
+    ,polarRatRev
     ,conj
     ,real
     ,imag
@@ -81,11 +88,40 @@
     )
     where
 
-import Data.List (nub)
+import Data.List
+    ( nub
+    )
 import Data.Ratio
+    ( (%)
+    , numerator
+    , denominator
+    )
 import Data.Complex
+    ( Complex(..)
+    , realPart
+    )
 import qualified Data.Map as M
-import Math.NumberTheory.Primes.Factorisation (factorise)
+    ( Map
+    , empty
+    , singleton
+    , lookup
+    , keys
+    , elems
+    , size
+    , fromList
+    , toList
+    , mapKeys
+    , filter
+    , insertWith
+    , delete
+    , map
+    , unionWith
+    , findWithDefault
+    , fromListWith
+    )
+import Math.NumberTheory.Primes.Factorisation
+    ( factorise
+    )
 
 -- | A cyclotomic number.
 data Cyclotomic = Cyclotomic { order  :: Integer
@@ -209,8 +245,10 @@
 
 -- | A complex number in polar form, with rational magnitude @r@ and rational angle @s@
 --   of the form @r * exp(2*pi*i*s)@; @polarRat r s@ is the same as @r * e q ^ p@,
---   where @s = p/q@.
-polarRat :: Rational -> Rational -> Cyclotomic
+--   where @s = p/q@.  This function is the same as 'polarRatRev'.
+polarRat :: Rational    -- ^ magnitude
+         -> Rational    -- ^ angle, in revolutions
+         -> Cyclotomic  -- ^ cyclotomic number
 polarRat r s
     = let p = numerator s
           q = denominator s
@@ -218,6 +256,31 @@
            True  -> fromRational r * e q ^ p
            False -> conj $ fromRational r * e q ^ (-p)
 
+-- | A complex number in polar form, with rational magnitude and rational angle
+--   in degrees.
+polarRatDeg :: Rational    -- ^ magnitude
+            -> Rational    -- ^ angle, in degrees
+            -> Cyclotomic  -- ^ cyclotomic number
+polarRatDeg r deg
+    = let s = deg / 360
+          p = numerator s
+          q = denominator s
+      in case p >= 0 of
+           True  -> fromRational r * e q ^ p
+           False -> conj $ fromRational r * e q ^ (-p)
+
+-- | A complex number in polar form, with rational magnitude and rational angle
+--   in revolutions.
+polarRatRev :: Rational    -- ^ magnitude
+            -> Rational    -- ^ angle, in revolutions
+            -> Cyclotomic  -- ^ cyclotomic number
+polarRatRev r s
+    = let p = numerator s
+          q = denominator s
+      in case p >= 0 of
+           True  -> fromRational r * e q ^ p
+           False -> conj $ fromRational r * e q ^ (-p)
+
 -- | Complex conjugate.
 conj :: Cyclotomic -> Cyclotomic
 conj (Cyclotomic n mp)
@@ -439,6 +502,20 @@
 cosDeg :: Rational -> Cyclotomic
 cosDeg d = let n = d / 360
                nm = abs (numerator n)
+               dn = denominator n
+               a = e dn^nm
+           in (a + conj a) / 2
+
+-- | Sine function with argument in revolutions.
+sinRev :: Rational -> Cyclotomic
+sinRev n = let nm = abs (numerator n)
+               dn = denominator n
+               a = e dn^nm
+           in fromRational(signum n) * (a - conj a) / (2*i)
+
+-- | Cosine function with argument in revolutions.
+cosRev :: Rational -> Cyclotomic
+cosRev n = let nm = abs (numerator n)
                dn = denominator n
                a = e dn^nm
            in (a + conj a) / 2